1. You have a large position in two bonds with similar credit risk (i.e., ignore credit risk). Bond A is priced at par yielding 6% with 20 years to maturity. Bond B has 20 years to maturity, coupon rate of 7% and yield of 6%. Assume a face value of 100 for both bonds and annual compounding.

a) Without making detailed calculations, can you guess which bond has a higher duration? b) Now calculate the durations of these bonds using excel. Were you right?

2. Information about Bonds A and B is given below. Construct a portfolio of these two bonds to match the value and duration of a 20-year, 8% coupon bond (Face value is $100). Bond is trading at par. Hint: First calculate the duration of the bond.

Bond A: 1 year zero coupon bond. Price=$94.26 for $100 face value. Bond B: 30 year zero coupon bond. Price $16.97 for $100 face value.

3. A brokerage firm purchases a 1000 face value coupon bond paying 6% per year on a semi-annual frequency. From that bond, the firm creates two bonds: A floater and an inverse floater. The face value of the floater is 700 and it pays LIBOR. What is the annual coupon rate of the inverse floater?

4. A 100 face value floater is paying LIBOR on a semiannual frequency. Today is t=0, 6 month LIBOR is equal to 6.78% (annualized), hence the first coupon 6 month from today will be $3.39.

a) What is the duration of the floater at t=0? b) What is its modified duration? c) What is its convexity?

5. The following information about bonds A, B, C, and D are given. Assume that bond prices admit no arbitrage opportunities. What is the modified duration of Bond D?

Cash Flow at the end of Bond Price Year 1 Year 2 Year 3

A 91 100 0 0 B 86 0 100 0 C 78 0 0 100 D ? 5 5 105